The term kinky sex is a kind of umbrella term to describe sex that is considered different, or not falling within social conventions of what 'regular sex' is. Since there is no universal definition of what is regular or normal, what gets defined as kinky sex is determined by the time, place, and people where the word is being used and where the sex is taking place.
In the past what was kinky was often associated with what are called fetishes. Kinky was a non-medical and in some cases non-pathologizing term for alternative sexualities.
The word kink is sometimes used alone to describe a particular sexual interest or way of thinking about sex (someone who has a fetish for leather might describe themselves as kinky, and someone who is always imagining complicated sexual scenarios may be called kinky by a friend or partner).
Some people use the word kinky to describe not just the kind of sex they have but their sexual identity. Thus some people identify as members of kink communities.
The term kinky sex is often contrasted with the term vanilla sex, which describes sex that does, supposedly, conform to the social conventions of the time and place where it's happening.
Source:
Oxford English Dictionary. Second edition, 1989; online version June 2011. Earlier version first published in New English Dictionary, 1901.
